We have developed and implemented an automated moment tensor inversion procedure to determine source parameters for southern California earthquakes. The method is based upon spectral-element simulations of regional seismic wave propagation in an integrated 3D southern California velocity model. Sensitivity to source parameters is determined by numerically calculating the Fréchet derivatives required for the moment tensor inversion. We minimize a waveform misfit function, and allow limited time shifts between data and corresponding synthetics to accommodate additional 3D heterogeneity not included in our model. The technique is applied to three recent southern California earthquakes: the 9 September 2001, ML 4.2 Hollywood event, the 22 February 2003, ML 5.4 Big Bear event, and the 14 December 2001, ML 4.0 Diamond Bar event. Using about half of the available three-component data at periods of 6 sec and longer, we obtain focal mechanisms, depths, and moment magnitudes that are generally in good agreement with estimates based upon traditional body-wave and surface-wave inversions.